Artículo de revista
Type II Blow-up in the 5-dimensional Energy Critical Heat Equation
Fecha
2019Registro en:
Acta Mathematica Sinica, English Series, Volumen 35, Issue 6, 2019, Pages 1027-1042
14398516
10.1007/s10114-019-8341-5
Autor
del Pino, Manuel
Musso, Monica
Wei, Jun Cheng
Institución
Resumen
We consider the Cauchy problem for the energy critical heat equation {ut=Δu+|u|4n−2uinRn×(0,T)u(⋅,0)=u0inRn in dimension n = 5. More precisely we find that for given points q 1 ,q 2 ,..,q k and any sufficiently small T > 0 there is an initial condition u 0 such that the solution u(x,t) of (0.1) blows-up at exactly those k points with rates type II, namely with absolute size ~(T-t) -α for α > 34. The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin–Talenti bubbles.